A NMPC-based spacecraft rendezvous maneuver with moving obstacles and variable prediction horizon

Since the first orbiting explorations, the rendezvous maneuver has become a fundamental operation in space missions. The operation consists of a spacecraft alignment to a specific target point, usually another spacecraft or some debris orbiting in the space. A successful rendezvous mission usually requires the determination of the trajectory, the speed, and the timing of the approaching spacecraft to ensure a safe and accurate approach. In this work thesis, the rendezvous problem is explained and analysed. Then, a control algorithm that guides an autonomous spacecraft to a requested position close to the target is proposed. Usually a spacecraft during the mission could encounter obstacles along the orbit, such as a meteorite to be dodged along the trajectory. In order to make the rendezvous mission more realistic, the task is performed including an obstacle like a sphere moving towards the spacecraft, so that the control algorithm is able to guide the spacecraft along its trajectory, satisfying the path constraints, and making him reach the target point. The obstacles are implemented within the optimization problem by augmenting the cost function with a suitable weighted penalty term that prevents the satellite to closely approach the obstacle. In the context of the space rendezvous maneuver, the Nonlinear Model Predictive Control (NMPC) appears as an appealing control tool, providing an optimal control law in presence of constraints on both input and state. The NMPC optimal control problem is solved by means of the Pontryagin Minimum (maximum in the original form) Principle (PMP). Furthermore, a slightly version of the NMPC, featuring a variable prediction horizon, is presented. The effectiveness of the two NMPC algorithms are then tested in simulation in a Matlab/Simulink environment, where the performance of the fixed and variable prediction horizons controllers are compared.